In a continuous-time representative investor economy with an exogenously given information process, asset prices are derived for alternative characterizations of the pricing kernel. In addition to the characterization of forward prices in a general representative investor economy a detailed analysis of forward prices for the HARA-class is given. In particular, analytical and numerical solutions of forward prices are derived for a representative investor with non-constant relative risk aversion. The derived asset prices are consistent with empirically well documented characteristics as mean reversion and random volatility. Hence, they are viable alternatives to the geometric Brownian motion.
equilibrium price processes displaced diffusion process random volatility mean-reversion